Summary
We propose a simple model of infection that enables to study the coincidence time of two random walkers on an arbitrary graph. By studying the coincidence time of a susceptible and an infected individual both moving in the graph we obtain estimates of the infection probability. The main result of this paper is to pinpoint the impact of the network topology on the infection probability.
Chapter PDF
Similar content being viewed by others
References
Barabási, A.-L., Albert, R.: Emergence of scaling in random networks. Science 286, 509–512 (1999)
Bollobás, B., Riordan, O.: The diameter of a scale-free random graph. Combinatorica 4, 5–34 (2004)
Chaintreau, A., Hui, P., Scott, J., Gass, R., Crowcroft, J., Diot, C.: Impact of human mobility on opportunistic forwarding algorithms. IEEE Trans. Mobile Comput. 6(6), 606–620 (2007)
Chung, F., Lu, L.: The average distances in random graphs with given expected degrees. Internet Math. 1, 91–114 (2003)
Daley, D.J., Gani, J.: Epidemic Modelling: An Introduction (Cambridge Studies in Mathematical Biology). Cambridge University Press, Cambridge (2001)
Datta, N., Dorlas, T.C.: Random walks on a complete graph: a model for infection. J. Appl. Prob. 41, 1008–1021 (2004)
Draief, M., Ganesh, A.: Spread of epidemics and rumours with mobile agents. Preprint (2008)
Faloutsos, M., Faloutsos, P., Faloutsos, C.: On power-law relationships of the Internet topology. In: Proceedings ACM SIGCOMM, 1999
Ganesh, A., Massoulié, L., Towsley, D.: The effect of network topology on the spread of epidemics. In: Proceedings of the IEEE INFOCOM, 2005
Mickens, J.W., Noble, B.D.: Modeling epidemic spreading in mobile environments. In: Proceedings of the 4th ACM Workshop on Wireless Security, pp. 77–86, 2005
Nekovee, M.: Worm epidemics in wireless ad hoc networks. New J. Phys. 9, 189 (2007)
Pittel, B.: On spreading a rumor. SIAM J. Appl. Math. 47(1), 213–223 (1987)
Rhodes, C.J., Nekovee, M.: The opportunistic transmission of wireless worms between mobile devices. arXiv arXiv:0802.2685v1 (2008)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Draief, M., Ganesh, A. (2010). Spread of Epidemics and Rumours with Mobile Agents. In: Fitt, A., Norbury, J., Ockendon, H., Wilson, E. (eds) Progress in Industrial Mathematics at ECMI 2008. Mathematics in Industry(), vol 15. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12110-4_128
Download citation
DOI: https://doi.org/10.1007/978-3-642-12110-4_128
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-12109-8
Online ISBN: 978-3-642-12110-4
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)